Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π.
800°
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 11
Use the formula ω = θ/t to find the value of the missing variable.
ω = 2π/3 radians per sec, t = 3 sec
Verified step by step guidance1
Identify the given variables and the formula: angular velocity \(\omega = \frac{\theta}{t}\), where \(\omega\) is angular velocity, \(\theta\) is the angular displacement in radians, and \(t\) is the time in seconds.
Substitute the known values into the formula: \(\omega = \frac{2\pi}{3}\) radians per second and \(t = 3\) seconds.
Rewrite the formula to solve for the missing variable \(\theta\): multiply both sides of the equation by \(t\) to get \(\theta = \omega \times t\).
Plug in the known values into the rearranged formula: \(\theta = \left(\frac{2\pi}{3}\right) \times 3\).
Simplify the expression to find \(\theta\), which represents the angular displacement in radians.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity (ω)
Angular velocity measures how fast an object rotates or revolves, expressed in radians per second. It is the rate of change of angular displacement over time, indicating how many radians the object covers each second.
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Angular Displacement (θ)
Angular displacement is the angle through which an object has rotated, measured in radians. It represents the total change in the angular position of the object during a given time interval.
Relationship Between Angular Velocity, Angular Displacement, and Time
The formula ω = θ / t relates angular velocity (ω), angular displacement (θ), and time (t). It shows that angular velocity equals the angular displacement divided by the time taken, allowing calculation of any one variable if the other two are known.
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Related Practice
Textbook Question
Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°
Textbook Question
Convert each radian measure to degrees.
5π/4
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Textbook Question
Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.
s = π/2
1
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Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°
1
views